1. Field of the Invention
The invention relates to a method for processing a 3-D measurement data set provided with seismic attributes, by means of a neural network, whereby a self-organizing map is trained with selected training data, and the data to be examined are classified according to the self-organizing map.
2. The Prior Art
Neural nets are a general term for a multitude of methods, which follow cognitive learning processes. A discrimination of these methods is based on the type of the learning. In so-called xe2x80x9csupervised learningxe2x80x9d, both the input and output are prescribed. In the network type that is relevant to this invention, i.e. the self-organizing map, the learning process is unsupervised, and serves to establish relations within the data, and to exploit them. Self-organizing maps originate from the attempt to develop explanations for neural processes in the brain. A stochastic model of that type is described, for example, in the publication Kohonen, T T., 1984, Self-Organisation and Associative Memory, 1. edition, Springer Verlag Heidelberg. It is further referred to the publication Ritter, H., Martinetz, T., and Schulten, K., 1991, Neuronale Netze (Neural Nets), Addison-Wesley.
In the model by Kohonen, all neurons are fully connected to the input. The intensity of the coupling to the input is variable, and is called the weight. Among themselves, the neurons are in each case coupled to their neighbors. If a training pattern is applied, all neurons enter into competition. The neuron specified by the largest similarity with the training pattern wins and adapts its weight towards the pattern. The similarity is computed, for example, by evaluating the scalar product between the training pattern and the weight vector. All other neurons adapt their weights with less strength. In this context, the adaptation strength depends on the distance of the individual neuron to the winner neuron on the neural map. The distance is determined by the number of neurons that are located between the neuron and the winner neuron. Now, further training patterns are applied, and the adaptation step is repeated for each pattern. In this process, the neurons organize themselves towards the training patterns. At the same time, the internal coupling causes all neurons to be involved in the process, and similar training patterns to be imaged to spatially neighbouring neurons.
After the training, the input patterns can be related to the neurons. In this respect, a winner neuron is determined for each training pattern. Desired characteristics of the training patterns can be assigned to the neurons as reference values. In the normal case, the number of input patterns is larger than the number of the neurons, so that several input patterns are imaged to one neuron. The reference values are then formed by the synthesis of the corresponding input patterns. A classification of unknown input data again takes place on the basis of the principle of competition. The pattern is applied to the net, and the reference pattern with the largest accordance is selected. Characteristics of the reference pattern, if existing, can then be transferred to the input pattern.
This generally known method is as well suited as a specialized evaluation method for the complex signal relations in seismic data, in which noisy, non-linear signals have to be processed. In the publication Trappe, H. 1994, Potential neuronaler Netze in der Kohlenwasserstoffexploration und -produktion (Potential of neural nets in the exploration and production of hydrocarbons), conference volume of the 14th Mintrop Seminar, the application potential of neural nets for the field of exploration and production of hydrocarbons is presented. In this publication, an example of a self-organizing neural process for the seismic reservoir characterisation is given as well.
From the publication Trappe, H., and Hellmich, C., xe2x80x9cAreal Prediction of Porosity Thickness from 3D Seismic Data by Means of Neural Networksxe2x80x9d (EAGE 59th Conference and Technical Exhibitionxe2x80x94Geneva, Switzerland, May 26-30 1977), the application of a neural, self-organizing type of a network for the prediction of the local reservoir quality from 3-D seismic data is known. The aim of the investigation is to establish from seismic data, or from attributes derived from seismic data, a map of porosity thicknesses along an interpreted horizon, here along the Rotliegendes. The amplitude, the lateral variation of the amplitude, and the acoustic impedance obtained from 3-D seismic inversion are used as input data. It is a disadvantage that the processing is limited to a narrowly limited zone, and that only a constant time, or an interpreted horizon is considered.
From the publication De Groot, P., Krajewski, P., and Bischoff, R., 1988, xe2x80x9cEvaluation of Remaining Oil Potential with 3D Seismic Using Neural Networksxe2x80x9d, EAGE Meeting and Exhibition, Leipzig, the use of an unsupervised neural network for the classification of the pore-fill from seismic data is known. In this context, short traces segments around the investigated horizon are used for the training, and for the classification.
Moreover, from U.S. Pat. No. 5,373,486, a method for the identification and classification of seismological sources, e.g. for the earthquake forecast, or for the verification of tests of nuclear weapons, is known. In this method, a signal arriving at the seismograph is transformed as a time series into a spectogram, and finally into a phase invariant representation by a two-dimensional Fourier transformation. These processed data are presented to a self-organising neural network.
From U.S. Pat. No. 5,940,777 a method for the automatic recognition of seismic patterns is known, in which single seismic trace segments are to be recognized by a self-organizing neural network, where the one-dimensional neural network (chain) exhibits just as much elements, as different patterns are available.
All previously mentioned, known methods have in common, that only single seismic data points (samples) or short seismic trace segments are used, which always refer to only one single seismic trace. It is a disadvantage that the local environment is not considered in the assignment of information derived from the seismic data.
PCT No. WO 97/39367 describes a method and an apparatus for the seismic signal processing and exploration, in which a seismic 3D volume is subdivided into cells. In the simplest case, these cells are cube-shaped. From the trace segments that are located in a cell and that amount to at least two in a cell, a correlation matrix is formed by sums of the differences between inner and outer products of the sets of values from the trace segments. The quotient formed by the highest eigenvalue of the matrix and the sum of all eigenvalues is then calculated as the measure of coherency. As the result, again a 3-D data volume is created, comprised of coherency values. Here sub-volumes are indeed considered, but without application of a neural net.
In the known methods, the training examples needed for the determination of the weights in the neural net, are extracted along a horizon or in a relatively narrow zone around the reservoir of interest. The remaining data is treated in the same way in the classification, which follows the training. The training examples are thus specifically selected, and for this selection, seismic data that was interpreted with other methods before, must be available for the determination of a horizon, or a reservoir. Moreover, the specific selection of training examples implies the risk that physical characteristics of the subsurface which strongly deviate from the selected characteristics, remain without consideration, or at least under-represented, in the classification.
In the state of art, the internal structure and the number of classes of the neural network are furthermore defined before the training. It often turns out, however, that a pre-defined network does not allow a representative classification of the measurement data. Then a multitude of training runs is required in order to find the correct parameters, namely the number of classes, the selection of attributes, and the selection of training examples, and in order to fix these parameters for the processing of the input data.
Therefore, it is an object of the invention to provide a method as mentioned initially, for the processing of a seismic measurement data set by means of a neural network, where in said method, an environment-related evaluation is achieved.
Because the training data are selected randomly from the measurement data set, an automated selection of training data shall be ensured. The selection of training examples is thus not confined to a horizon, or to a chosen reservoir zone, so that no prior interpretation takes place. Patterns, or training data, respectively, with extreme value ranges are also entered into the training by the random choice. Situations which are considered to have very low probability, are thus considered as well. The training data thus comprise a much larger dynamic range, so that trends in amplitude behavior, for example, can be considered as well. If the training data are selected randomly from a pre-defined time/depth window of the measurement data set, the selection can be confined to a limited region of the total 3D volume, in an evaluation aiming at this limited region.
Through the processing of the measurement data by means of a spatial environment of each measurement data point, it is achieved, that the lateral change of the seismic signal is considered as well besides the vertical distribution of amplitude information, as a significant parameter for the characterisation of the subsurface. Hence, because of the knowledge of the lateral changes of the geology, statements on the thickness of sand bodies, or of the sedimentary environment, respectively, can be determined from the distribution of the values in the sub-volume. The method according to the invention allows a classification of seismic sub-volumes, or of sub-volumes provided with attributes derived from the seismic data, in an automatic evaluation. In this context, a volume assigned to the seismic data point is considered as input data. After-completion of the training process, a classification result can be assigned to each data point. In the automatic evaluation, similar seismic sub-volumes are then assigned to the same, or to neighboring classes.
Through the evaluation in sub-volumes, it is taken into account, among other things, that the reflected seismic energy cannot be assigned to exactly one point of the subsurface, due to the limits of seismic resolution, and to the used numerical methods. On the contrary, this point is better described by its local environment, and in this respect the consideration of dependencies in a sub-volume is advantages as compared to idealized one-dimensional earth models.
Each sub-volume preferably consists of a measurement data point (reference point), and a pre-defined number of measurement data points (samples) from the environment of the reference point, and a pre-defined, relative location of said data points with respect to the reference point. For a pre-defined, fixed number of data points in the sub-volume, the dimension of the weight vector is defined equal to this number, and is not altered any more. The interaction between the neurons as determined by the weight vectors, thus considers the environmental dependencies in the sub-volume.
The sub-volumes have, for example, square-stone shape, e.g. with 3xc3x973xc3x973 data points, or the shape of an ellipsoid with its main axes centered at the reference point. Thus a practicable and uniformly balanced consideration of the data points in the environment of the investigated data point (reference point) is achieved. The square-stone or cubic shape facilitates the assignment of data to sub-volumes in the common 3-D measurement data sets with a cubic structure.
The neural network is trained with a pre-defined number of training data.
Nevertheless, in order to carry out a selection with respect to certain characteristics in the investigated 3-D measurement data set, the selection of the training data can be confined to pre-defined inlines and crosslines, and the training data can be randomly selected from a target layer of the measurement data set that is defined by two enclosing horizons. This procedure shall achieve, for example, a restriction of the selection of training data to geologically reasonable regions. In addition, the use of non-uniform acquisition methods within the 3-D measurement data set, e.g. dynamite seismics, vibrator seismics, land seismicsxe2x80x94shallow water seismics, etc., can be considered by a correspondingly assigned, i.e. restricted selection of the training data in the evaluation.
A dedicated selection of training data can further be achieved by determining characteristic parameter values for all sub-volumes of the measurement data set, and by randomly selecting the training data by means of pre-defined criteria that are derived from the characteristic parameter values.
As characteristic parameters, it may be chosen, for example: mean amplitude, mean absolute amplitude, coherency, dip (layer inclination), azimuth, proximity to faults, difference from smallest and largest amplitude value, etc . . . In this context, several characteristic parameters may be combined for the determination of selection criteria.
In order to obtain a representative selection of training examples from the investigated 3-D measurement data set, the distribution of characteristic parameter values from all sub-volumes of the measurement data set is determined, and the training data are selected such that the distribution of the characteristic parameter values from the training data corresponds to the total distribution.
Because the distribution of characteristic parameter values from all sub-volumes is determined from the measurement data set, and that the training data are selected randomly such that the distribution of the characteristic parameter values from the training data corresponds to a distribution chosen previously, a non-representative selection of training data is deliberately presented. This non-representative selection can be desired, for example, if the classification objective is the detection of faults, whereas the data points in the proximity of faults constitute a very small portion only of the measurement data set.
In order to avoid a misdirection of the mutual dependency in the neural net at the start of the training, the weight vectors are filled with random numbers at the start of the training.
In case of similar geological situations, the weight vectors may be adopted by way of exception from an earlier, similar computation. The neural network can also be initialized by a training result that was created already before, such that the total course of the training must not be repeated, e.g. in the case of an addition of new training data.
By carrying out the training for such a duration, until a certain error criterion is fulfilled, a high quality of the data evaluation can be ensured. As an error criterion in this context, the mean error with respect to the used input data can be determined as the sum of the individual errors of each single input pattern, divided through the total number of input patterns. If the value falls below a pre-defined maximum error, the training is stopped.
If this error criterion is not fulfilled, the number and/or the connection of the neurons is altered in the course of the training. Preferably, the number of neurons is increased at first in this context, and in a second step, the network connections are increased. As an alternative, the distance between the weight vectors of two neighboring neurons can as well be chosen as the criterion for the insertion of neurons, and of connections.
In a neural net with a two-dimensional grid configuration, a neighborhood with sets of four, our eight neurons can be formed, except for the neurons located at the edge. However, the two-dimensional grid configuration can exhibit any arbitrary network connections.
If the neural net is arranged in the form of a torus, a structure is defined in which negative edge effects are avoided. If a neural net is formed as a chain, each neuron possesses two neighbors, except for the first, and last neuron. It is advantageous in this context, that an assignment of ordinal numbers in increasing order to the neurons is possible, and thus, a graphical representation, for example a color scale, can easily be assigned as well. In a further embodiment, several chains can be provided.
Alternatively, the neural net can be embodied as a three-dimensional grid. In this context, a connection of neighbouring neurons by means of weight vectors is conceivable as a neighbourhood with a set of six neurons and with connective relations that are arranged orthogonally only, in an orthogonal grid configuration.
Because each neuron possesses a unique ordinal number, and to each measurement data point, the corresponding ordinal number of the winner neuron, and an individual error, given as the distance between the measurement data point and the winner neuron, are assigned, a unique relation of a pair of result values to each measurement data point (sample) is provided. Concerning the individual error of an input pattern, the distance of the input datum to all neurons is determined. Then, the smallest distance is selected as individual error; whereas the neuron connected to this smallest distance simultaneously is the winner neuron, which represents the corresponding ordinal number. Common distance measures are the scalar product of vectors, or the Euclidian distance.
The result data set which is provided with ordinal numbers and error values, and from which maps or slices can be extracted for a 2D display, is preferably entered in digital form to further processing.
In order to allow a graphical representation of the ordinal numbers that are assigned in the result data set, the ordinal numbers of the neurons are computed as polar coordinates in case of a two-dimensional configuration of the neurons. In this context, the angle co-ordinate of a neuron determines a hue, and the radius determines a saturation. The origin of the co-ordinate system is defined in the center of the neural net. The color intensity can be selected constant, or equal to the saturation, for example. Thus, each ordinal number occurring in the neural net is represented by the hue -and saturation in a visually recognizable way. Neurons that are neighbors to each other, as-well exhibit similar hues and similar saturations.
In case of a three-dimensional configuration of the neurons, the hue, saturation, and intensity are correspondingly derived from ordinal numbers computed in spherical co-ordinates. Here as well, the origin of the co-ordinate system is defined in the centre of the configuration of the neurons.
Besides the 3D measurement data set provided with seismic amplitudes, other data with attributes derived from seismic data can as well be used as input data sets, e.g. a volume of acoustic impedance, coherency, dip and/or azimuth.